In the past few decades, the petroleum industry has invested heavily in the development of marine seismic survey techniques that yield knowledge of subterranean formations beneath a body of water in order to find and extract valuable resources, such as oil. High-resolution seismic images of a subterranean formation are essential for quantitative seismic interpretation and petroleum reservoir monitoring. For a typical marine seismic survey, a survey vessel tows a seismic source, and the same vessel, or another vessel, tows one or more streamers that form a seismic data acquisition surface below the surface of the water and above a subterranean formation to be surveyed for resources. The survey vessel typically contains seismic acquisition equipment, such as navigation control, seismic source control, seismic receiver control, and recording equipment. The seismic source control activates a seismic source, which is typically an array of source elements, such as air guns or marine vibrators, that produces acoustic signals at selected times. Each acoustic signal is a sound wave that travels down through the water and into the subterranean formation. At each interface between different types of rock, a portion of the sound wave may be transmitted and another portion may be reflected back into the body of water as a wavefield that propagates upward toward the water surface. The streamers towed behind the vessel are typically elongated, cable-like structures equipped with a number of seismic receivers or multi-component sensors that detect pressure and/or particle motion wavefields associated with the wavefields reflected back into the water from the subterranean formation.
Sound waves that propagate down into the formation, undergo a single reflection from an interface, and are subsequently detected by seismic receivers are called “primary reflections.” However, the water surface may act as a near perfect reflector by reflecting sound waves back down toward the subterranean formation. As a result, each reflection from the water surface may generate a reverberation of multiple reflections. These reflections are called “surface-related multiples” Multiple reflections may also be generated by sound waves reflected within the subsurface without reflections from the water surface. These reflections are called “internal multiples.” Seismic data generated by a receiver typically records the primary reflections and the surface-related and internal multiples. As a result, seismic data-processing techniques that depend on the primary reflections are often obscured or contaminated by the surface-related and internal multiples, making analysis of the formation a challenge. Geophysicist, petroleum engineers, and others working in the petroleum industry continue to seek systems and methods that attenuate the contribution of surface-related and internal multiples in seismic data.